Further results on modified harmonic functions in three dimensions

dc.contributor.authorLeutwiler, Heinz
dc.date.accessioned2021-06-07
dc.date.available2023-10-11T11:36:33Z
dc.date.created2021
dc.date.issued2021-06-07
dc.description.abstractThe Weinstein equation tΔu+k∂u∂t=0, with k∈ℤ, considered in ℝ3=(x,y,t), is a modification of the classical Laplace equation Δu=0. Its solutions are called k‐modified harmonic functions. Whereas for positive integers k the Weinstein equation is relatively well understood, little is known if the parameter k is negative. The main result of this article is the statement that in case the negative integers are even, i.e., k=−2ℓ,ℓ∈ℕ, we still have a Fischer‐type decomposition. For k=0, the classical harmonic functions, this decomposition is well known. But also in case k∈ℕ, a Fischer‐type decomposition holds true, a Fischer‐type decomposition holds true. Surprisingly in case k=−3,k=−5, or k=−7 and probably in all higher negative odd cases, the decomposition doesn't hold. In case k=−1, we give a complete description of the vector space Hnk(ℝ3) of homogeneous k‐modified harmonic polynomials of degree n in ℝ3. Such a result is also at hand in case k∈ℕ. Finally, in case k=0 of the classical harmonic functions, we give a description of the vector space Hn(ℝ3)=Hn0(ℝ3).en
dc.identifier.citationMathematical Methods in the Applied Sciences (2021). <https://onlinelibrary.wiley.com/doi/10.1002/mma.7277>
dc.identifier.doihttps://doi.org/10.1002/mma.7277
dc.identifier.opus-id16505
dc.identifier.urihttps://open.fau.de/handle/openfau/16505
dc.identifier.urnurn:nbn:de:bvb:29-opus4-165057
dc.language.isoen
dc.publisherJohn Wiley & Sons Ltd.
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.de
dc.subjectgeneralized axially symmetric potentials
dc.subjectmodified spherical harmonics
dc.subjectspherical harmonics
dc.subject.ddcDDC Classification::5 Naturwissenschaften und Mathematik :: 51 Mathematik :: 510 Mathematik
dc.titleFurther results on modified harmonic functions in three dimensionsen
dc.typearticle
dcterms.publisherFriedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
local.date.prevpublished2021-02-16
local.journal.titleMathematical Methods in the Applied Sciences
local.sendToDnbfree*
local.subject.fakultaetNaturwissenschaftliche Fakultät
local.subject.importimport
local.subject.sammlungUniversität Erlangen-Nürnberg / Eingespielte Open Access Artikel / Eingespielte Open Access Artikel 2021
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